$\sum\limits_{k=0}^{2 }{{(2k+2)}}=$
Solution: What is the question asking for? $\sum$ tells us to find the sum. The question is asking for the sum of the values of $2k+2$ from $k = 0$ to $k = 2$. Evaluating $\begin{aligned} \sum\limits_{k=0}^{2 }{({2k+2})}&= (2( 0)+2) + (2( 1)+2) + (2( 2)+2) \\\\ &= 2 + 4 + 6 \\\\ &= 12\end{aligned}$ The answer $\sum\limits_{k=0}^{2 }{({2k+2})}=12$